Question: Solve for $x$ and $y$ using elimination. ${-4x-y = -41}$ ${3x+y = 32}$
Solution: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $-y$ and $y$ cancel out. $-x = -9$ $\dfrac{-x}{{-1}} = \dfrac{-9}{{-1}}$ ${x = 9}$ Now that you know ${x = 9}$ , plug it back into $\thinspace {-4x-y = -41}\thinspace$ to find $y$ ${-4}{(9)}{ - y = -41}$ $-36-y = -41$ $-36{+36} - y = -41{+36}$ $-y = -5$ $\dfrac{-y}{{-1}} = \dfrac{-5}{{-1}}$ ${y = 5}$ You can also plug ${x = 9}$ into $\thinspace {3x+y = 32}\thinspace$ and get the same answer for $y$ : ${3}{(9)}{ + y = 32}$ ${y = 5}$